known_trajectory_map

[Peter230655]

Neville contacted me yesterday. With W(t) a state variable, he seems to need X(t) = W(t) - W(t - A) with A, fixed, 0 < A < t.
I cannot find a hack for this.
IF one could make a known_trajectory to depend on the solutions, this might solve such problems.
What I mean is like this: obj_grad(free) is a function (I think so anyway) of the intermediate results during the iteration.
if the same thing could be done for a known trajectory I believe this could help to solve such problems.
Of course I have no idea, whether this would only be difficult or impossible,

Thanks!

[moorepants]

Passing a function to known_trajectory_map gives access to free inside the function. But you then have to write the derivative of the function too.

[Peter230655]

Like we are doing it with numerical trajectories in e.g. plot_hilly_race ?
Pretty dumb of me not to think of this!

[Peter230655]

I played around a bit, seems to work in principle.
I do not have a simulation, though where this would make sense.

[Peter230655]

I think, Neville has seen it, so I close it,

[Peter230655]

I doubt my "idea" works, at least I do not get it to work.
Basic problem, as I understood Neville is this:
The battery of an electric car can give the current p(t). The higher p(t) the stronger the motor drives the car.
However, due to overheating the total current output in any time interval of length time_delay must be limited to P_max.
Also, there is not recharging of the battery (p(t) < 0) in case breaking takes place. Hence:
$P(t) = \int_{t - time_{delay}}^t p(s) ds \leq P_{max}$, where $p(s) = 0$ if $p(s) \leq 0$
Of course $\dfrac{P(t)}{dt} = P(t) - P(t - time_{delay})$

I had this "idea":

make P(t), P(t).diff(t) known trajectories depending on the state variable p(t)
add X - P(t) to the eoms.
add a bound X < $P_{max}$

and I had thought, that opty would adjust p(t) so the bound for X is met.
However, this does not seem to work with the three examples I tried.
It does not throw an error, but it does not converge.

Just adding X - P(t) to the eoms, but not even bounding X prevents my examples from converging.